I have a couple of suggestions:
1: Home depot by me has some metal shelving units consisting of 4 shelves and some cross bracing. I got one of these and some 3/4" plywood. Cut the plywood to fit the shelving and then stacked the brinks boxes on the bottom shelves. You can store some good weight this way. I store the unit in an extra closet. The reason for the plywood is to strengthen the shelves to prevent them from deforming under the weight of the pennies. Start at the bottom and use just the bottom 2 shelves. The top shelves can be used to store lighter things. You can store some good weight.
2: I also purchased a locking metal storage unit and put it in my garage. Cut a piece of 3/4" plywood to fit the interior. This strengthens the bottom shelf and you can store a lot of weight and will have it under lock and key and somewhat secured. I can store both pennies and nickels and they will be out of sight of prying eyes. I hope for the best that the load doesn't shift and causes problems with opening and closing the door.
Stay away from plastic shelving because the shelves will deform if you don't have 2 x 4's under the bottom shelf and you really can't put to much weight on the 2nd shelf.
The problem as I see it with milk crates is moving around the weight if you have to restack them. By stacking the brinks boxes on end you can fit 9 into a milk case but at 17 pounds a box you'll be moving 153 pounds at a time and that'll get real tedious real fast and I don't know how many you would be willing stack one on top of another before the fun goes away. You may stack 4 crates on top of one another before your arms give out. But you will get an upper body work out if you move them more than once. The other thing there is a little dead space and if you stack the milk crates on end I don't know how many you can stack up this way before the bottom crate starts to crack.
When you have a lot of pennies weight does begin to become an important factor. Nickels at 22 pounds per box is even more so. The way that I store my nickels is in .30 caliber ammo can. You can put $188 in a can and these cans come with a convenient carrying handle that won't tear off and the can will not deform under weight, they have consistent measurments and you can stack them real easily. You can store pennies in them also but I don't know how many penny rolls you can put in a can. But I feel that you can put more than $25 in a can.
Stay away from the .50 caliber or 20mm boxes due to weight considerations. Russian 7.62 boxes are to heavy also. You can get .30 caliber ammo cans for about $5 and they last forever. They also have a multiitude of uses around the home. ie small parts storage, tool storage, store craft parts, I am thinking about switching over the ammo cans and getting rid of the shelving unit
Your wife probably won't want to help you move them at all.

Don't look back. Something may be gaining on you.
Neither a penny or a nickel is worth face value anymore.
I'm just a poor wayfaring stranger.